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R1: IF X
11
is S1 AND X
12
is CE AND X
13
is CE AND X
14
is B1 THEN Y
1
is B2.
Note that in the above rule
X
11
,
X
12
,
X
13
, and
X
14
actually represent the first,
second, third and fourth inputs respectively of the system, whereas
Y
1
represents
the corresponding single output from the system.
S2 S1 CE B1 B2
1.0
0.8
0.6
0.4
0.2
0.0
X
lo
X
21
X
22
X
23
X
24
Y
2
X
hi
X
ki
Figure 4.3(b).
Division of input and output range in fuzzy regions
Furthermore, according to Figure 4.3(b), this gives [
X
21
(0.6 in S1, max),
X
22
(0.8 in
S1, max),
X
23
(0.8 in CE, max),
X
24
(0.6 in B1, max );
Y
2
(0.8 in B2, max)],
i.e.
rule
R2 is
R2: IF X
21
is S1 AND X
22
is S1 AND X
23
is CE AND X
24
is B1 THEN Y
2
is B2.
Note that, as in the previous rule, here also
X
21
,
X
22
,
X
23
, and
X
24
actually represent
the first, second, third and fourth inputs respectively to the system, and
Y
2
represents the corresponding single output from the system.
Step 3:
rules degree assignment
The large number of data pairs available generate a large number of rules, some of
them being conflicting rules. To each rule the degree will be assigned and the
conflicting rules with the highest degree retained. For example, the degree of the
rule
Rule: IF
x
1
is
A
AND
x
2
is
B
AND
x
3
is
C
AND
x
4
is
D
, THEN
y
is
E
is as follows:
D
(
Rule
) = P
A
(
x
1
). P
B
(
x
2
). P
C
(
x
3
). P
D
(
x
4
). P
E
(
y
),
so that the rules R1 and R2 above have the degrees:
D
(
Rule
1) = P
S1
(
X
11
). P
CE
(
X
12
). P
CE
(
X
13
). P
B1
(
X
14
). P
B2
(
Y
1
)
= (0.8).(0.6).(0.8).(0.8).(0.6) = 0.18432,
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